Absolute convergence of Fourier integrals and Lipschitz classes

B.I. Peleshenko (Dnipropetrovsk State Agrarian and Economic University)


The necessary and sufficient conditions, in terms of Fourier transforms $$$\hat{f}$$$ of functions $$$f \in L^1(\mathbb{R})$$$, are obtained for $$$f$$$ to belong to the Lipschitz classes $$$H^{\omega}(\mathbb{R})$$$ and $$$h^{\omega}(\mathbb{R})$$$.


Fourier transform; Fourier integral; modulus of continuity; Lipschitz classes


Stein I., Weiss G. Introduction to Fourier analysis on Euclidean spaces, Mir, Moscow, 1974; 333 p. (in Russian)

Moricz F. "Absolutely convergent Fourier integrals and classical function spaces", Arch. Math., 2008; 91: pp. 49-62. doi:10.1007/s00013-008-2626-8

DOI: https://doi.org/10.15421/241115



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ISSN (Online): 2664-5009
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